CDN-266: The Jeans Test — Modified Jeans Equation for Dwarf Spheroidals with RAR-Validated Interpolation

Solves the spherical isotropic Jeans equation for 22 MW dwarf spheroidals using the RAR-validated interpolation function ν(x) = 1/(1−exp(−√x)) from CDN-265. Plummer stellar profile with Abel projection to luminosity-weighted σ_los. Results: Jeans recovers 3/22 within 20% (Fornax 1.06, Leo I 0.99, Leo II 0.82) versus Wolf estimator 0/22. The Jeans integral improves every prediction by 10–15× over Wolf by accumulating ν-enhanced gravity over the full radial profile (effective boosts 6–139× in σ²). MOND simple and RAR ν produce identical σ_Jeans, confirming GCFT = MOND at dSph scale. Remaining gap is luminosity-correlated (1.3× for massive classicals to 57× for faint ultrafaints). The CDN-265 "two-sector" finding is reframed: substantially an estimator artefact, with the residual deficit matching the known MOND dSph problem (external field effect, tidal stripping, anisotropy). Pre-registers CDN-267 for MW external field effect and velocity anisotropy.

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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-06-17
DOI
https://doi.org/10.5281/zenodo.20727395
Primary Topic
Cosmology and Gravitation Theories
Type
article
Field-Weighted Citation Impact
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article

CDN-266: The Jeans Test — Modified Jeans Equation for Dwarf Spheroidals with RAR-Validated Interpolation

Nicky Joseph Hubertus Catharina Hacquier
Zenodo (CERN European Organization for Nuclear Research)
Cosmology and Gravitation Theories
article

CDN-266: The Jeans Test — Modified Jeans Equation for Dwarf Spheroidals with RAR-Validated Interpolation

Nicky Joseph Hubertus Catharina Hacquier
article en

Abstract

Solves the spherical isotropic Jeans equation for 22 MW dwarf spheroidals using the RAR-validated interpolation function ν(x) = 1/(1−exp(−√x)) from CDN-265. Plummer stellar profile with Abel projection to luminosity-weighted σ_los. Results: Jeans recovers 3/22 within 20% (Fornax 1.06, Leo I 0.99, Leo II 0.82) versus Wolf estimator 0/22. The Jeans integral improves every prediction by 10–15× over Wolf by accumulating ν-enhanced gravity over the full radial profile (effective boosts 6–139× in σ²). MOND simple and RAR ν produce identical σ_Jeans, confirming GCFT = MOND at dSph scale. Remaining gap is luminosity-correlated (1.3× for massive classicals to 57× for faint ultrafaints). The CDN-265 "two-sector" finding is reframed: substantially an estimator artefact, with the residual deficit matching the known MOND dSph problem (external field effect, tidal stripping, anisotropy). Pre-registers CDN-267 for MW external field effect and velocity anisotropy.

Zenodo (CERN European Organization for Nuclear Research)
Dynamique du noyau (FR)
Openalex Percentile: Top 7%
Cosmology and Gravitation Theories
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